Math - Investigatory project

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SO LETS SAY I AM CREATING THE CODE OF PINS HERE AND YOU ARE SUPPOSED TO FIGURE IT OUT. SO I CAN ARRANGE A TOTAL OF FOUR PINS, WHICH MEANS MY r value is 4.
AND THERE ARE FOUR COLOURS OF RED, GREEN , BLUE AND YELLOW OF EACH 4 PINS FOR ME TO MAKE THE CODE WITH. SO MY n value is 4*4 = 16
SO THE NUMBER OF COMBINATIOSN OF CODE I CAN MAKE IS nCr = 16C4. WHICH IS EQUAL TO 140 COMBINATIONS OF CODE
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ARRANGING IT IN DIFFERENT ORDER, I GET A COMBINATION OF 8C4, where n = 8 and r = 4. Doing the calculation we get, 70 codes
LETS FIND THE PROBALITY THAT I WILL ARRANGE A CODE OF 2 BLUE AND 2 RED PINS. SO I NEED TO FIRST FIND NO OF COMBINATIONS OF THIS CODE.
SO THE PROBALITY OF THIS TYPE OF CODE IS; P(2BLUE AND 2 RED PINS CODE) = 8C4/16C4 = 1/2. THAT'S IT.
ALL YOU GOT A REMEBER IS THE OVER COMBINATIONS WILL BE THE DINOMINATOR AND THE TYPE OF COMINATION WILL COME IN NUMINATOR. I HOPE YOU WERE ABLE TO UNDERSTAND IT.
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THANK YOU SO MUCH FOR EXPLAINING THIS REMA. NOW I TOTALLY UNDERSTAND IT. I THINK I WILL BE ABLE TO SOLVE SUMS RELATED TO THIS NOW.

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